Related papers: Multi-pulse phase resetting curve
We consider the Yamada model for an excitable or self-pulsating laser with saturable absorber, and study the effects of delayed optical self-feedback in the excitable case. More specifically, we are concerned with the generation of stable…
The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of…
We present a simple approach to predict the main features of optical spectra affected by self-phase modulation (SPM), which is based on regarding the spectrum modification as an interference effect. A two-wave interference model is found…
Two-stroke relaxation oscillations consist of two distinct phases per cycle - one slow and one fast - which distinguishes them from the well-known van der Pol-type 'four-stroke' relaxation oscillations. This type of oscillation can be found…
We report our investigation on the input signal amplification in unidirectionally coupled monostable Duffing oscillators in one- and two-dimensions with first oscillator alone driven by a weak periodic signal. Applying a perturbation theory…
Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small…
In this paper we propose a novel geometric method, based on singular perturbations, to approximate isochrones of relaxation oscillators and predict the qualitative shape of their (finite) phase response curve. This approach complements the…
A nonperturbative correction to the thermal nucleation rate of critical bubbles in a first order phase transition is estimated. The correction originates from large-amplitude fluctuations which may be present before the transition occurs.…
In a recent paper [Chaos 30, 073139 (2020)] we analyzed an extension of the Winfree model with nonlinear interactions. The nonlinear coupling function Q was mistakenly identified with the non-infinitesimal phase-response curve (PRC). Here,…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
We investigate the phase response properties of the Hindmarsh-Rose model of neuronal bursting using burst phase response curves (BPRCs) computed with an infinitesimal perturbation approximation and by direct simulation of synaptic input.…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
We consider networks of weakly pulse-coupled identical oscillators. In an effort to resolve a long-standing problem, we develop an analytic condition on the infinitesimal phase response curve (iPRC) for synchronized dynamic behaviour,…
Nonlinear resonant structures consisting of coupled ring resonators can be modeled by difference-differential equations that take into account non-instantaneous Kerr response and the effect of loss. We present a simple and efficient…
In many real-world oscillator systems, the phase response curves are highly heterogeneous. However, dynamics of heterogeneous oscillator networks has not been seriously addressed. We propose a theoretical framework to analyze such a system…
I study how pulse to pulse phase coherence in a pulse train can survive super-broadening by extreme self phase modulation (SPM). Such pulse trains have been used in phase self-stabilizing schemes as an alternative to using a feedback…
In this letter, we propose for the first time a method of abstracting the PPV (Perturbation Projection Vector) characteristic of the up-to-date memristor-based oscillators. Inspired from biological oscillators and its characteristic named…
The phase response curve (PRC) is an important measure representing the interaction between oscillatory elements. To understand synchrony in biological systems, many research groups have sought to measure PRCs directly from biological cells…
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…
The emergence of collective synchronization was reproduced long ago by Winfree in a classical model consisting of an ensemble of pulse-coupled phase oscillators. By means of the Ott-Antonsen ansatz, we derive an exact low-dimensional…